Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
def min_row():
    ans = 0
    for i in range(n):
        ans += min(a[i])
    return ans


def min_col():
    ans = 0
    for i in range(m):
        mm = 10000
        for j in range(n):
            mm = min(mm, a[j][i])
        ans += mm
    return ans


def remove_cols():
    ans = 0
    min_col = [0] * m
    for i in range(m):
        min_col[i] = 1000
        for j in range(n):
            min_col[i] = min(min_col[i], a[j][i])
        ans += min_col[i]
        for j in range(n):
            a[j][i] -= min_col[i]
    return ans, min_col


def remove_rows():
    ans = 0
    min_row = []
    for i in range(n):
        min_row.append(min(a[i]))
        ans += min_row[-1]
        for j in range(m):
            a[i][j] -= min_row[i]
    return ans, min_row


n, m = list(map(int, input().split()))
a = []
s = 0

for i in range(n):
    row = list(map(int, input().split()))
    a.append(row)
    s += sum(row)

rows = min_row()
cols = min_col()

if rows == 0 and cols == 0:
    if s == 0:
        print(0)
        exit()
    else:
        print(-1)
        exit()

if cols == 0 or (rows != 0 and (s - rows * m) % n == 0 and ((s - cols * n) % m != 0 or (s - rows * m) // n + rows < (s - cols * n) // m + cols)):
    ans, min_row = remove_rows()
    ans1, min_col = remove_cols()
else:
    ans1, min_col = remove_cols()
    ans, min_row = remove_rows()

ans += ans1

for row in a:
    for ai in row:
        if ai != 0:
            print(-1)
            exit()

print(ans)
for i in range(n):
    for j in range(min_row[i]):
        print("row", i + 1)
for i in range(m):
    for j in range(min_col[i]):
        print("col", i + 1)